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I am looking for an analytical solution of the following quadratic programming problem : $$ \min_x x^TA x, s.t. 1^T.x = 1, 0 \le x \le 1 $$

where A is positive definite.

I am not looking for a QP solver, I am aware of their existence and their performance. I am looking for an analytical solution, or a theorem proving that there is none.

Is anybody aware of any solution? Or a starting point?

Thank you very much in advance

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